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A003592
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Numbers of the form 2^i*5^j with i, j >= 0.
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40
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1, 2, 4, 5, 8, 10, 16, 20, 25, 32, 40, 50, 64, 80, 100, 125, 128, 160, 200, 250, 256, 320, 400, 500, 512, 625, 640, 800, 1000, 1024, 1250, 1280, 1600, 2000, 2048, 2500, 2560, 3125, 3200, 4000, 4096, 5000, 5120, 6250, 6400, 8000, 8192, 10000
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listen;
history;
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internal format)
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OFFSET
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1,2
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COMMENTS
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These are the natural numbers whose reciprocals are terminating decimals. - David Wasserman, Feb 26 2002
A132726(a(n),k)=0 for k<=a(n); A051626(a(n))=0; A132740(a(n))=1; A132741(a(n))=a(n). - Reinhard Zumkeller, Aug 27 2007
Where record values greater than 1 occur in A165706: A165707(n)=A165706(a(n)). [From Reinhard Zumkeller, Sep 26 2009]
Also numbers that are divisible by neither 10k-7, 10k-3, 10k-1 nor 10k+1, for all k > 0. [From Robert G. Wilson v, Oct 26 2010]
A204455(5*a(n)) = 5, and only for these numbers. - From Wolfdieter Lang, Feb 04 2012
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LINKS
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R. Zumkeller, Table of n, a(n) for n = 1..1000
Eric Weisstein's World of Mathematics, Regular Number
Eric Weisstein's World of Mathematics, Decimal Expansion
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MAPLE
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isA003592 := proc(n)
if n = 1 then
true;
else
return (numtheory[factorset](n) minus {2, 5} = {} );
end if;
end proc:
A003592 := proc(n)
option remember;
if n = 1 then
1;
else
for a from procname(n-1)+1 do
if isA003592(a) then
return a;
end if;
end do:
end if;
end proc: # R. J. Mathar, Jul 16 2012
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MATHEMATICA
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fQ[n_] := PowerMod[10, n, n] == 0; Select[ Range@ 10000, fQ] (* Robert G. Wilson v, Jan 12 2012 *)
fQ[n_] := Union[ MemberQ[{1, 3, 7, 9}, # ] & /@ Union@ Mod[ Rest@ Divisors@ n, 10]] == {False}; fQ[1] = True; Select[ Range@ 10000, fQ] [From Robert G. Wilson v, Oct 26 2010]
mx = 14; Sort@ Flatten@ Table[2^i*5^j, {i, 0, mx}, {j, 0, Log[5, 2^(mx - i)]}] (* Or *)
Union@ Flatten@ NestList[{2#, 4#, 5#} &, 1, 7] (* Robert G. Wilson v, Apr 16 2011 *)
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PROG
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(PARI) list(lim)=my(v=List(), N); for(n=0, log(lim+.5)\log(5), N=5^n; while(N<=lim, listput(v, N); N<<=1)); vecsort(Vec(v)) \\ Charles R Greathouse IV, Jun 28 2011
(Sage)
def isA003592(n) :
return [] == filter(lambda d: d != 2 and d != 5, prime_divisors(n))
@CachedFunction
def A003592(n) :
if n == 1 : return 1
k = A003592(n-1) + 1
while not isA003592(k) : k += 1
return k
[A003592(n) for n in (1..48)] # Peter Luschny, Jul 20 2012
(MAGMA) [n: n in [1..10000] | PrimeDivisors(n) subset [2, 5]]; // Bruno Berselli, Sep 24 2012
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CROSSREFS
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Sequence in context: A181666 A067943 A067937 * A192716 A159765 A018653
Adjacent sequences: A003589 A003590 A003591 * A003593 A003594 A003595
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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